ES4F0 - Advanced Control Systems

Module content and teaching

Principal aims

The module objective is to teach various methods of synthesizing control systems for real-world complex dynamic systems such that the desired end user objectives are met satisfactorily. • The dynamic systems considered in this course are real-world systems that can be represented through systems of ordinary differential equations. • The complexities include large system dimensions (leading to computational challenges), nonlinearities, and time-delays. • Techniques to test whether the end user objectives are feasible will be taught first and then the techniques for synthesizing requisite controllers will be introduced. • To ensure that the students understand how to apply the concepts and techniques for real-world applications, the module includes a case study project on synthesizing controller for a process control and a detailed case study involving theoretical questions and a programming assignment. In this context, the module aims to first introduce mathematical paradigms so that the task of meeting the end-user objectives can be posed as a constrained optimization problem. • Here, the basics of state-space control, linear programming, and LMI programming will be introduced. The module then aims to cover some landmark results on the infeasibility of design objectives (e.g., the waterbed theory, limitations due to RHP poles, limitations due to time delays). The module then aims to teach algorithms to check the feasibility of the performance objectives. In the final 5 weeks, the module aims to cover the salient features of different computational methods, along with associated software programming, of synthesizing a controller (PID controller, H-infinity controller, and L1 adaptive controller) whose robustness properties can be specified a priori by the end user.

Principal learning outcomes

By the end of the course, the student will be able to do the following: • Given a dynamic system expressed using ordinary differential equations, check whether the end user objectives are feasible or not. • Pose the controller synthesis problem as a constrained optimization problem using state space representation (note: here, the controller can be PID or optimal or H-infinity or L1 adaptive). • Use linear programming and LMI programming to solve this problem, and write the associated software code.

Departmental link

Other essential notes

• Pre-Course material on software programming and Linear Programming will be made available to the students 1 week before the lectures starts. • Pre-Course material on elementary controller synthesis will be made available to the students 1 week before the lectures start. Assessed work to be passed based on overall average rather than individually